This is set theory, not real analysis. The first one should be straightforward. Your notation is sort of hard to follow for 2, but that is the correct containment direction you concluded. Can you try coming up with a simple counterexample for the reverse direction? Consider perhaps a set A containing distinct elements a1 and a2, and let A1 = {a1} and A2 = {a2} and think of the simplest functions possible.